A test for a certain disease is found to be 96 accurate mean

A test for a certain disease is found to be 96% accurate, meaning that it will correctly diagnose the disease in 96 out of 100 people who have the ailment. The test is also 96% accurate for a negative result, meaning that it will correctly exclude the disease in 96 out of 100 people who do not have the ailment. For a certain population segment, the incidence of the disease is 6%.

If a person tests positive, find the probability that the person actually has the disease (Hint: define appropriate events and use Bayes Theorem);

Solution

Let A be the event that the test is positive, B1 be the event that a person is infected and B2 be the event that a person is not infected.

P(A/B1) = 96/100

P(A/B2) = 4/100

P(B1) = 6/100

P(B2) = 94/100

P(B1/A)

= 96/100 * 6/100/(96/100 * 6/100) + (4/100 * 94/100)

= 0.6050

= 60.5%